Elevation gain is a measure of vertical distance. It is a common form of measurement in events like this.
For example, ultramarathons will often tout something like “20,000 feet of elevation gain!”. This does not imply the ultramarathon is run up a 20,000 foot mountain but rather implies cumulative elevation. This is what Everesting implies, as well.
Altitude is generally the distance from sea level and implies other factors in this context, namely atomosphere thinning.